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From: rvdb@hou2c.UUCP (R.VANDERBEI)
Newsgroups: net.math
Subject: Re: Counter-Intuitive Sequences
Message-ID: <595@hou2c.UUCP>
Date: Mon, 3-Feb-86 22:33:35 EST
Article-I.D.: hou2c.595
Posted: Mon Feb  3 22:33:35 1986
Date-Received: Wed, 5-Feb-86 01:49:30 EST
References: <748@garfield.UUCP>
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 23

> Consider the following sequence:
> 
> 		1, 2, 4, 8, 16,....
> 
> what is the next term ?	
> 
> Invariably the response is "32".
> This however does not have to be the case and an alternate sequence arises
> very naturally. Consider the sequence of n where n is the number of regions
> the interior of a circle can be divided into using k lines where k starts
> at 0. If you do that for the first five k you get the above sequence.
> Suggestive isn't it ? However it turns out that for k=6 n=31 and the 
> intuitive result falls flat on its face.
> The "correct" answer (in this sense) is "31".
> However any IQ test in which you answered "31" you would probably be put
> down as a low-grade moron then and there so when in doubt answer "32" !
>
>					Robert Janes


It seems to me that the sequence breaks down when k=3 and n=7.
Perhaps you meant to state the same problem for a sphere in 4-space
using hyperplanes for lines.